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The problem you've uploaded involves the daily price changes for two shopkeepers, Mohan and Sohan, and it asks for the maximum number of days \( n \) such that at least one of their prices is less than 400 after \( n \) days.

### Summary of the Price Change Rules:
- **Initial prices**: Mohan's price = 130, Sohan's price = 140.
- **Daily price change conditions**:
  - If **Mohan's price** is more than **Sohan's price**:  
    - Mohan increases by 10.
    - Sohan increases by 40.
  - If **Mohan's price** is less than or equal to **Sohan's price**:  
    - Mohan increases by 30.
    - Sohan increases by 10.

We need to calculate the prices of Mohan's and Sohan's apples for each day, and determine the maximum value of \( n \) such that at least one of their prices is less than 400.

Let's solve this systematically by iterating through the days and updating their prices based on the given conditions. I will compute the price changes step by step until one of the prices reaches or exceeds 400.After computing the prices for each day, we find that:

- Mohan's prices over the days:  
  \[ 130, 160, 170, 200, 230, 240, 270, 280, 310, 340, 350, 380, 390 \]
  
- Sohan's prices over the days:  
  \[ 140, 150, 190, 200, 210, 250, 260, 300, 310, 320, 360, 370, 410 \]

The price of one of the shopkeepers (Sohan) exceeds 400 after **12 days**. Therefore, the maximum value of \( n \) such that at least one of their prices is less than 400 is:

\[
n = 12
\]

Would you like further details on the steps, or any clarifications?

Here are some follow-up questions you might consider:
1. How do the price increments change dynamically based on the conditions?
2. What if we reverse the initial prices of Mohan and Sohan?
3. How would the result change if the price increments were altered?
4. Could we set up a general formula for this scenario?
5. What happens if the starting prices were significantly different?

**Tip**: Breaking complex problems into small daily increments helps in understanding long-term patterns.

Mohan and Sohan are two shopkeepers in the market of Panipat. Both of them own Apple shops. Both of them decided to introduce their own price strategy (for per kg) for 'n' days, starting from day 1 to day 'n' and it was observed that: At the starting of a day, if the price of Mohan's apple is more than that of Sohan's, then by the beginning of next day Mohan increases the price of his apples by 10 while Sohan increases by 40. And, if the price of Mohan’s apple is less than or equal to that of Sohan’s, then by the beginning of next day Mohan increases the price of his apples by 30 while Sohan increases by 10. Given that, at the beginning of Day 1, the price of Mohan’s apples was 130 and Sohan’s was 140. At the end of the nth day, the price of the apples of at least one of the shopkeepers (i.e. Mohan or Sohan) was less than 400, then what is the maximum value of 'n'?

Solve a real-world problem involving price increments between two shopkeepers, Mohan and Sohan, over 'n' days. Understand how linear patterns and inequalities are used to find the maximum value of 'n' where at least one shopkeeper’s price remains under 400. A practical algebra problem suitable for Grades 9-10.

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